GK Per and EX Hya: Intermediate polars with small magnetospheres

Abstract: Observed hard X-ray spectra of intermediate polars are determined mainly by the accretion flow velocity at the white dwarf surface, which is normally close to the free-fall velocity. This allows to estimate the white dwarf masses as the white dwarf mass-radius relation M-R and the expected free-fall velocities at the surface are well known. This method is widely used, however, derived white dwarf masses M can be systematically underestimated because the accretion flow is stopped at and re-accelerates from the magnetospheric boundary R_m, and therefore, its velocity at the surface will be lower than free-fall.To avoid this problem we computed a two-parameter set of model hard X-ray spectra, which allows to constrain a degenerate M - R_m dependence. On the other hand, previous works showed that power spectra of accreting X-ray pulsars and intermediate polars exhibit breaks at the frequencies corresponding to the Keplerian frequencies at the magnetospheric boundary. Therefore, the break frequency \nu_b in an intermediate polar power spectrum gives another relation in the M - R_m plane. The intersection of the two dependences allows, therefore, to determine simultaneously the white dwarf mass and the magnetospheric radius. To verify the method we analyzed the archival Suzaku observation of EX Hya obtaining M /M_sun= 0.73 \pm 0.06 and R_ m / R = 2.6 \pm 0.4 consistent with the values determined by other authors. Subsequently, we applied the same method to a recent NuSTAR observation of another intermediate polar GK~Per performed during an outburst and found M/M_sun = 0.86 \pm 0.02 and R_ m / R = 2.8 \pm 0.2. The long duration observations of GK Per in quiescence performed by Swift/BAT and INTEGRAL observatories indicate increase of magnetosphere radius R_m at lower accretion rates.